x^2+1.8x-0.4=0

Solution for x^2+1.8x-0.4=0 equation:

Simplifying
x2 + 1.8x + -0.4 = 0

Reorder the terms:
-0.4 + 1.8x + x2 = 0

Solving
-0.4 + 1.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 1.8x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 1.8x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 1.8x + x2 = 0 + 0.4
1.8x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
1.8x + x2 = 0.4

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = 0.4 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = 0.4 + 0.81

Combine like terms: 0.4 + 0.81 = 1.21
0.81 + 1.8x + x2 = 1.21

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 1.21

Calculate the square root of the right side: 1.1

Break this problem into two subproblems by setting 
(x + 0.9) equal to 1.1 and -1.1.

Subproblem 1
x + 0.9 = 1.1

Simplifying
x + 0.9 = 1.1

Reorder the terms:
0.9 + x = 1.1

Solving
0.9 + x = 1.1

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = 1.1 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = 1.1 + -0.9
x = 1.1 + -0.9

Combine like terms: 1.1 + -0.9 = 0.2
x = 0.2

Simplifying
x = 0.2

Subproblem 2
x + 0.9 = -1.1

Simplifying
x + 0.9 = -1.1

Reorder the terms:
0.9 + x = -1.1

Solving
0.9 + x = -1.1

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = -1.1 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = -1.1 + -0.9
x = -1.1 + -0.9

Combine like terms: -1.1 + -0.9 = -2
x = -2

Simplifying
x = -2

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2, -2}